Subgroups — C₂×#23777090 #35196183

Order 20224.

9502 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777090	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099240	C₂	1	8	yes	maximal, complemented
3	C₂×#19099204	C₂	1	8	yes	maximal, complemented
4	C₂×#19099153	C₂	1	4	yes	maximal, complemented
5	C₂×#19099125	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19099076	C₂	1	4	yes	maximal, complemented
7	C₂²×#14579131	C₂	1	2	yes	maximal, complemented
8	C₂×#19099036	C₂	1	2	yes	maximal, complemented
9	C₂²×C₂²⋊C₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#543×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₇₉	C₂²	1	1	yes	characteristic
12	C₂²×#11929625	C₂²	1	4	yes	complemented
13	C₂³×D₃₁₆	C₂²	1	4	yes	complemented
14	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	—
15	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
16	#19099240	C₂²	1	128	yes	complemented
17	#19099204	C₂²	1	128	yes	complemented
18	#19099153	C₂²	1	64	yes	complemented
19	#19099125	C₂²	1	16	yes	complemented
20	C₂×#14579156	C₂²	1	8	yes	complemented
21	C₂×#14579150	C₂²	1	8	yes	complemented
22	#19099076	C₂²	1	64	yes	complemented
23	C₂×#14579146	C₂²	1	8	yes	complemented
24	C₂×#14579146	C₂²	1	8	yes	complemented
25	C₂×#14579145	C₂²	1	4	yes	complemented
26	C₂×#14579137	C₂²	1	4	yes	complemented
27	C₂×#14579136	C₂²	1	8	yes	complemented
28	C₂×#14579136	C₂²	1	4	yes	complemented
29	C₂×#14579135	C₂²	1	4	yes	complemented
30	C₂×#14579131	C₂²	1	8	yes	—
31	C₂×#14579131	C₂²	1	4	yes	complemented
32	C₂×#14579131	C₂²	1	4	yes	complemented
33	C₂×#14579131	C₂²	1	32	yes	complemented
34	C₂×#14579131	C₂²	1	4	yes	complemented
35	#19099036	C₂²	1	32	yes	complemented
36	C₂×#14579123	C₂²	1	8	yes	complemented
37	C₂×C₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
38	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	8	yes	complemented
39	C₂×#14579119	C₂²	1	4	yes	complemented
40	C₂×#14579117	C₂²	1	4	yes	complemented
41	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
42	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
43	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
44	C₂×C₂²⋊C₄×D₇₉	C₂²	1	8	yes	complemented
45	C₂×C₂²⋊C₄×D₇₉	C₂²	1	16	yes	complemented
46	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
47	#543×C₇₉	C₂²	1	16	yes	complemented
48	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	8	yes	complemented
49	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	4	yes	complemented
50	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
52	C₂⁴×D₇₉	—	2	8	no	—
53	C₂⁴×D₇₉	—	4	8	no	—
54	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
55	C₂⁴×D₇₉	C₂³	1	4	yes	—
56	C₂⁴×D₇₉	C₂³	1	8	yes	—
57	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
58	C₂⁴×D₇₉	C₂³	1	2	yes	—
59	C₂×#11929625	—	4	16	no	—
60	C₂×#11929625	C₂³	1	32	yes	complemented
61	C₂²×D₃₁₆	—	4	16	no	—
62	C₂²×D₃₁₆	C₂³	1	8	yes	—
63	C₂²×D₃₁₆	C₂³	1	8	yes	—
64	C₂²×D₃₁₆	C₂³	1	32	yes	complemented
65	C₂²×D₃₁₆	C₂³	1	4	yes	complemented
66	C₂²×C₂²⋊D₇₉	—	2	16	no	—
67	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
68	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
69	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
70	C₂³×Dic₇₉	C₂³	1	2	yes	—
71	C₂³×Dic₇₉	C₂³	1	2	yes	—
72	C₂²×C₄×D₇₉	—	4	8	no	—
73	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
74	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
75	C₂²×C₄×D₇₉	C₂³	1	16	yes	complemented
76	C₂²×C₄×D₇₉	C₂³	1	8	yes	complemented
77	#14579156	C₂³	1	64	yes	complemented
78	#14579150	C₂³	1	64	yes	complemented
79	#14579146	C₂³	1	64	yes	complemented
80	#14579146	C₂³	1	64	yes	complemented
81	#14579145	C₂³	1	32	yes	complemented
82	#14579137	C₂³	1	32	yes	complemented
83	#14579136	C₂³	1	64	yes	complemented
84	#14579136	C₂³	1	32	yes	complemented
85	#14579135	C₂³	1	32	yes	complemented
86	#14579131	C₂³	1	64	yes	—
87	#14579131	C₂³	1	32	yes	complemented
88	#14579131	C₂³	1	32	yes	complemented
89	#14579131	C₂³	1	32	yes	complemented
90	#14579123	C₂³	1	64	yes	complemented
91	C₄×C₂²⋊D₇₉	C₂³	1	64	yes	complemented
92	(C₂²⋊D₇₉)⋊C₄	C₂³	1	64	yes	complemented
93	#14579119	C₂³	1	32	yes	complemented
94	#14579117	C₂³	1	32	yes	complemented
95	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	complemented
96	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	complemented
97	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
99	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
100	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
101	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
102	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	complemented
103	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	32	yes	complemented
104	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
105	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
106	C₂²⋊C₄×D₇₉	C₂³	1	64	yes	complemented
107	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
108	C₂×C₄×Dic₇₉	C₂³	1	8	yes	complemented
109	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₇₉	C₂³	1	4	yes	complemented
111	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
112	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
113	C₂²⋊Q₈×C₇₉	C₂³	1	32	yes	complemented
114	C₂²⋊Q₈×C₇₉	C₂³	1	64	yes	complemented
115	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	complemented
116	C₂×C₄⋊C₄×C₇₉	C₂³	1	8	yes	complemented
117	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	—
122	C₂³×D₇₉	—	2	4	no	—
123	C₂³×D₇₉	—	2	8	no	—
124	C₂³×D₇₉	—	2	16	no	—
125	C₂³×D₇₉	—	2	4	no	—
126	C₂³×D₇₉	—	2	32	no	—
127	C₂³×D₇₉	—	2	8	no	—
128	C₂³×D₇₉	—	2	16	no	—
129	C₂³×D₇₉	—	4	32	no	—
130	C₂³×D₇₉	—	4	8	no	—
131	C₂³×D₇₉	—	4	4	no	—
132	C₂³×D₇₉	—	4	8	no	—
133	C₂³×D₇₉	—	4	64	no	—
134	C₂³×D₇₉	C₂⁴	1	2	yes	—
135	C₂³×D₇₉	C₂⁴	1	4	yes	—
136	C₂³×D₇₉	C₂⁴	1	4	yes	—
137	C₂³×D₇₉	C₂⁴	1	16	yes	—
138	C₂³×D₇₉	C₂⁴	1	2	yes	—
139	C₂³×D₇₉	C₂⁴	1	4	yes	—
140	C₂³×D₇₉	C₂⁴	1	8	yes	—
141	#11929625	—	4	64	no	—
142	C₂×D₃₁₆	—	2	32	no	—
143	C₂×D₃₁₆	—	4	8	no	—
144	C₂×D₃₁₆	—	4	16	no	—
145	C₂×D₃₁₆	—	4	64	no	—
146	C₂×D₃₁₆	C₂⁴	1	32	yes	—
147	C₂×D₃₁₆	C₂⁴	1	32	yes	—
148	C₂×D₃₁₆	C₂⁴	1	16	yes	complemented
149	C₂×C₂²⋊D₇₉	—	2	16	no	—
150	C₂×C₂²⋊D₇₉	—	2	16	no	—
151	C₂×C₂²⋊D₇₉	—	2	64	no	—
152	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
153	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
154	C₂²×Dic₇₉	—	2	8	no	—
155	C₂²×Dic₇₉	—	4	4	no	—
156	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
157	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
158	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
159	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
160	C₂×C₄×D₇₉	—	2	16	no	—
161	C₂×C₄×D₇₉	—	4	16	no	—
162	C₂×C₄×D₇₉	—	4	8	no	—
163	C₂×C₄×D₇₉	—	4	32	no	—
164	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
165	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
166	C₂×C₄×D₇₉	C₂⁴	1	32	yes	complemented
167	C₄⋊Dic₇₉	C₂⁴	1	16	yes	complemented
168	Dic₇₉⋊C₄	C₂⁴	1	32	yes	complemented
169	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
170	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
171	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
172	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
173	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	complemented
174	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	complemented
175	C₄×Dic₇₉	C₂⁴	1	32	yes	complemented
176	C₂⁴×C₇₉	—	4	4	no	—
177	C₂⁴×C₇₉	#41	1	8	yes	complemented
178	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
179	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
180	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
181	C₂×Q₈×C₇₉	—	4	8	no	—
182	C₂×Q₈×C₇₉	C₂⁴	1	16	yes	complemented
183	C₂²×C₄×C₇₉	—	4	4	no	—
184	C₂²×C₄×C₇₉	—	4	8	no	—
185	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
186	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
188	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
189	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
190	C₄⋊C₄×C₇₉	C₂⁴	1	32	yes	complemented
191	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
192	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
193	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
194	C₂³×C₇₉	—	2	4	no	—
195	C₂³×C₇₉	—	2	8	no	—
196	C₂³×C₇₉	—	4	16	no	—
197	C₂³×C₇₉	—	4	8	no	—
198	C₂³×C₇₉	C₂×#41	1	8	yes	—
199	C₂³×C₇₉	C₂×#41	1	4	yes	—
200	C₂³×C₇₉	C₂×#41	1	16	yes	complemented
201	C₂³×C₇₉	C₂⁵	1	4	yes	—
202	C₂³×C₇₉	C₂⁵	1	2	yes	—
203	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
204	C₂²×D₇₉	—	2	32	no	—
205	C₂²×D₇₉	—	2	8	no	—
206	C₂²×D₇₉	—	2	4	no	—
207	C₂²×D₇₉	—	2	4	no	—
208	C₂²×D₇₉	—	2	16	no	—
209	C₂²×D₇₉	—	2	8	no	—
210	C₂²×D₇₉	—	2	32	no	—
211	C₂²×D₇₉	—	2	8	no	—
212	C₂²×D₇₉	—	2	4	no	—
213	C₂²×D₇₉	—	2	16	no	—
214	C₂²×D₇₉	—	2	8	no	—
215	C₂²×D₇₉	—	2	16	no	—
216	C₂²×D₇₉	—	2	32	no	—
217	C₂²×D₇₉	—	4	16	no	—
218	C₂²×D₇₉	—	4	8	no	—
219	C₂²×D₇₉	—	4	16	no	—
220	C₂²×D₇₉	—	4	64	no	—
221	C₂²×D₇₉	—	4	128	no	—
222	C₂²×D₇₉	—	4	16	no	—
223	C₂²×D₇₉	—	8	16	no	—
224	C₂²×D₇₉	H(5,𝔽₂)	1	8	yes	—
225	C₂²×D₇₉	C₂⁵	1	4	yes	—
226	C₂²×D₇₉	C₂⁵	1	8	yes	—
227	C₂²×D₇₉	C₂⁵	1	4	yes	—
228	Q₈×C₇₉	—	4	16	no	—
229	C₂×C₄×C₇₉	—	2	8	no	—
230	C₂×C₄×C₇₉	—	2	16	no	—
231	C₂×C₄×C₇₉	—	4	8	no	—
232	C₂×C₄×C₇₉	—	4	16	no	—
233	C₂×C₄×C₇₉	C₂⁵	1	16	yes	—
234	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
235	C₂²⋊D₇₉	—	2	32	no	—
236	C₂²⋊D₇₉	—	2	32	no	—
237	C₂×Dic₇₉	—	2	16	no	—
238	C₂×Dic₇₉	—	2	8	no	—
239	C₂×Dic₇₉	—	2	8	no	—
240	C₂×Dic₇₉	—	4	8	no	—
241	C₂×Dic₇₉	C₂⁵	1	8	yes	—
242	C₂×Dic₇₉	C₂⁵	1	8	yes	—
243	D₃₁₆	—	2	64	no	—
244	D₃₁₆	—	4	32	no	—
245	D₃₁₆	—	4	16	no	—
246	C₄×D₇₉	—	2	32	no	—
247	C₄×D₇₉	—	4	16	no	—
248	C₄×D₇₉	—	4	32	no	—
249	C₂²×C₇₉	—	2	8	no	—
250	C₂²×C₇₉	—	2	4	no	—
251	C₂²×C₇₉	—	2	8	no	—
252	C₂²×C₇₉	—	2	16	no	—
253	C₂²×C₇₉	—	4	16	no	—
254	C₂²×C₇₉	C₂²×#41	1	4	yes	—
255	C₂²×C₇₉	C₂²×#41	1	8	yes	—
256	C₂²×C₇₉	C₂²×#41	1	2	yes	—
257	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
258	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
259	C₂×D₇₉	—	2	32	no	—
260	C₂×D₇₉	—	2	4	no	—
261	C₂×D₇₉	—	2	4	no	—
262	C₂×D₇₉	—	2	16	no	—
263	C₂×D₇₉	—	2	8	no	—
264	C₂×D₇₉	—	2	4	no	—
265	C₂×D₇₉	—	2	8	no	—
266	C₂×D₇₉	—	2	16	no	—
267	C₂×D₇₉	—	4	64	no	—
268	C₂×D₇₉	—	4	16	no	—
269	C₂×D₇₉	—	4	8	no	—
270	C₂×D₇₉	—	4	16	no	—
271	C₂×D₇₉	—	8	16	no	—
272	C₂×D₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
273	C₄×C₇₉	—	2	8	no	—
274	C₄×C₇₉	—	2	16	no	—
275	Dic₇₉	—	2	8	no	—
276	Dic₇₉	—	2	8	no	—
277	C₂×#3490	—	79	1	no	maximal, Sylow
278	C₂×C₇₉	—	2	4	no	—
279	C₂×C₇₉	—	2	8	no	—
280	C₂×C₇₉	#3490	1	4	yes	complemented
281	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
282	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
283	D₇₉	—	2	8	no	—
284	D₇₉	—	4	4	no	—
285	D₇₉	—	4	8	no	—
286	#3490	—	79	32	no	—
287	C₂×#551	—	79	8	no	—
288	C₂×#546	—	79	8	no	—
289	C₂×#543	D₇₉	1	1	yes	characteristic, complemented
290	C₂×#538	—	79	4	no	—
291	C₂×#534	—	79	1	no	—
292	C₂×#525	—	79	4	no	—
293	C₂²×#120	—	79	2	no	—
294	C₂×#518	—	79	2	no	—
295	C₂³×C₂²⋊C₄	—	79	1	no	—
296	C₇₉	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
297	C₂⁶	—	79	1	no	—
298	C₂²×#41	—	79	4	no	—
299	C₂³×D₄	—	79	2	no	—
300	C₂³×D₄	—	79	4	no	—
301	C₂⁴×C₄	—	79	2	no	—
302	#551	—	79	128	no	—
303	#546	—	79	128	no	—
304	#543	C₂×D₇₉	1	16	yes	complemented
305	#538	—	79	64	no	—
306	#534	—	79	16	no	—
307	C₂×#126	—	79	8	no	—
308	C₂×#124	—	79	8	no	—
309	#525	—	79	64	no	—
310	C₂×#123	—	79	8	no	—
311	C₂×#123	—	79	8	no	—
312	C₂×#123	—	79	4	no	—
313	C₂×C₂²⋊Q₈	—	79	4	no	—
314	C₂×C₂²⋊Q₈	C₂×D₇₉	1	4	yes	complemented
315	C₂×C₂²⋊Q₈	C₂×D₇₉	1	8	yes	complemented
316	C₂×#121	—	79	4	no	—
317	C₂×#121	—	79	4	no	—
318	C₂×#121	—	79	8	no	—
319	C₂×#120	—	79	4	no	—
320	C₂×#120	—	79	4	no	—
321	C₂×#120	—	79	8	no	—
322	C₂×#120	—	79	32	no	—
323	C₂×#120	—	79	4	no	—
324	#518	—	79	32	no	—
325	C₂×C₄×D₄	—	79	8	no	—
326	C₂×C₄×D₄	—	79	8	no	—
327	C₂×C₄×D₄	—	79	8	no	—
328	C₂×#117	—	79	4	no	—
329	C₂×#117	—	79	4	no	—
330	C₂²×C₂²⋊C₄	—	79	1	no	—
331	C₂²×C₂²⋊C₄	—	79	2	no	—
332	C₂²×C₂²⋊C₄	—	79	4	no	—
333	C₂²×C₂²⋊C₄	—	79	8	no	—
334	C₂²×C₂²⋊C₄	—	79	16	no	—
335	C₂²×C₂²⋊C₄	—	79	4	no	—
336	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
338	C₂⁵	—	316	8	no	—
339	C₂⁵	—	79	1	no	—
340	C₂⁵	—	79	8	no	—
341	C₂⁵	—	79	2	no	—
342	C₂⁵	—	79	4	no	—
343	C₂⁵	—	79	1	no	—
344	C₂⁵	—	158	8	no	—
345	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
346	C₂×#41	—	316	16	no	—
347	C₂×#41	—	79	32	no	—
348	C₂²×Q₈	C₂²×D₇₉	1	4	yes	complemented
349	C₂²×D₄	—	316	16	no	—
350	C₂²×D₄	—	79	4	no	—
351	C₂²×D₄	—	79	4	no	—
352	C₂²×D₄	—	79	16	no	—
353	C₂²×D₄	—	79	4	no	—
354	C₂²×D₄	—	79	8	no	—
355	C₂²×D₄	—	79	32	no	—
356	C₂²×D₄	—	79	8	no	—
357	C₂²×D₄	—	158	16	no	—
358	C₂³×C₄	—	316	8	no	—
359	C₂³×C₄	—	79	2	no	—
360	C₂³×C₄	—	79	4	no	—
361	C₂³×C₄	—	79	16	no	—
362	C₂³×C₄	—	79	8	no	—
363	C₂³×C₄	—	79	2	no	—
364	C₂³×C₄	—	79	4	no	—
365	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
366	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
367	#126	—	79	64	no	—
368	#124	—	79	64	no	—
369	#123	—	79	64	no	—
370	#123	—	79	64	no	—
371	#123	—	79	32	no	—
372	C₂²⋊Q₈	—	79	32	no	—
373	C₂²⋊Q₈	C₂²×D₇₉	1	32	yes	complemented
374	C₂²⋊Q₈	C₂²×D₇₉	1	64	yes	complemented
375	#121	—	79	32	no	—
376	#121	—	79	32	no	—
377	#121	—	79	64	no	—
378	#120	—	79	32	no	—
379	#120	—	79	32	no	—
380	#120	—	79	64	no	—
381	#120	—	79	32	no	—
382	C₄×D₄	—	79	64	no	—
383	C₄×D₄	—	79	64	no	—
384	C₄×D₄	—	79	64	no	—
385	#117	—	79	32	no	—
386	#117	—	79	32	no	—
387	C₂×C₄⋊C₄	—	79	8	no	—
388	C₂×C₄⋊C₄	—	79	4	no	—
389	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	complemented
390	C₂×C₄⋊C₄	C₂²×D₇₉	1	8	yes	complemented
391	C₂×C₂²⋊C₄	—	79	4	no	—
392	C₂×C₂²⋊C₄	—	79	8	no	—
393	C₂×C₂²⋊C₄	—	79	8	no	—
394	C₂×C₂²⋊C₄	—	79	16	no	—
395	C₂×C₂²⋊C₄	—	79	8	no	—
396	C₂×C₂²⋊C₄	—	79	8	no	—
397	C₂×C₂²⋊C₄	—	79	8	no	—
398	C₂×C₂²⋊C₄	—	79	32	no	—
399	C₂×C₂²⋊C₄	—	79	8	no	—
400	C₂×C₂²⋊C₄	—	79	64	no	—
401	C₂×C₂²⋊C₄	—	79	32	no	—
402	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
404	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂²×D₇₉	1	16	yes	—
407	C₂×C₄²	—	79	8	no	—
408	C₂⁴	—	4	4	no	—
409	C₂⁴	—	316	4	no	—
410	C₂⁴	—	316	8	no	—
411	C₂⁴	—	316	8	no	—
412	C₂⁴	—	316	64	no	—
413	C₂⁴	—	316	32	no	—
414	C₂⁴	—	79	4	no	—
415	C₂⁴	—	79	8	no	—
416	C₂⁴	—	79	16	no	—
417	C₂⁴	—	79	2	no	—
418	C₂⁴	—	79	4	no	—
419	C₂⁴	—	79	2	no	—
420	C₂⁴	—	79	4	no	—
421	C₂⁴	—	158	16	no	—
422	C₂⁴	—	158	8	no	—
423	C₂⁴	—	158	4	no	—
424	C₂⁴	—	158	16	no	—
425	C₂⁴	—	158	32	no	—
426	C₂⁴	—	158	8	no	—
427	C₂⁴	—	158	4	no	—
428	C₂⁴	#11929625	1	8	yes	complemented
429	C₂⁴	C₂³×D₇₉	1	2	yes	—
430	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
431	C₂⁴	C₂³×D₇₉	1	4	yes	—
432	#41	—	316	64	no	—
433	C₂×Q₈	—	4	8	no	—
434	C₂×Q₈	C₂³×D₇₉	1	16	yes	complemented
435	C₂×D₄	—	316	16	no	—
436	C₂×D₄	—	316	8	no	—
437	C₂×D₄	—	316	64	no	—
438	C₂×D₄	—	79	16	no	—
439	C₂×D₄	—	79	16	no	—
440	C₂×D₄	—	79	32	no	—
441	C₂×D₄	—	79	16	no	—
442	C₂×D₄	—	79	32	no	—
443	C₂×D₄	—	158	32	no	—
444	C₂×D₄	—	158	16	no	—
445	C₂×D₄	—	158	16	no	—
446	C₂×D₄	—	158	64	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	—	316	8	no	—
450	C₂²×C₄	—	316	16	no	—
451	C₂²×C₄	—	316	32	no	—
452	C₂²×C₄	—	316	4	no	—
453	C₂²×C₄	—	79	8	no	—
454	C₂²×C₄	—	79	16	no	—
455	C₂²×C₄	—	79	32	no	—
456	C₂²×C₄	—	79	8	no	—
457	C₂²×C₄	—	79	4	no	—
458	C₂²×C₄	—	79	4	no	—
459	C₂²×C₄	—	79	16	no	—
460	C₂²×C₄	—	158	16	no	—
461	C₂²×C₄	—	158	8	no	—
462	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
463	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
464	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
465	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
466	C₄⋊C₄	—	79	32	no	—
467	C₄⋊C₄	—	79	16	no	—
468	C₄⋊C₄	C₂³×D₇₉	1	16	yes	complemented
469	C₄⋊C₄	C₂³×D₇₉	1	32	yes	complemented
470	C₂²⋊C₄	—	79	16	no	—
471	C₂²⋊C₄	—	79	32	no	—
472	C₂²⋊C₄	—	79	32	no	—
473	C₂²⋊C₄	—	79	32	no	—
474	C₂²⋊C₄	—	79	32	no	—
475	C₂²⋊C₄	—	79	32	no	—
476	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
477	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
478	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
479	C₄²	—	79	32	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	4	16	no	—
483	C₂³	—	4	8	no	—
484	C₂³	—	316	16	no	—
485	C₂³	—	316	64	no	—
486	C₂³	—	316	8	no	—
487	C₂³	—	316	16	no	—
488	C₂³	—	316	16	no	—
489	C₂³	—	316	128	no	—
490	C₂³	—	79	8	no	—
491	C₂³	—	79	4	no	—
492	C₂³	—	79	4	no	—
493	C₂³	—	79	8	no	—
494	C₂³	—	632	16	no	—
495	C₂³	—	158	32	no	—
496	C₂³	—	158	16	no	—
497	C₂³	—	158	32	no	—
498	C₂³	—	158	16	no	—
499	C₂³	—	158	8	no	—
500	C₂³	—	158	8	no	—
501	C₂³	—	158	8	no	—
502	C₂³	—	158	32	no	—
503	C₂³	—	158	4	no	—
504	C₂³	—	158	16	no	—
505	C₂³	—	158	4	no	—
506	C₂³	—	158	8	no	—
507	C₂³	—	158	4	no	—
508	C₂³	C₂×#11929625	1	8	yes	—
509	C₂³	C₂×#11929625	1	4	yes	—
510	C₂³	C₂×#11929625	1	16	yes	complemented
511	C₂³	C₂⁴×D₇₉	1	4	yes	—
512	C₂³	C₂⁴×D₇₉	1	2	yes	—
513	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
514	Q₈	—	4	16	no	—
515	D₄	—	316	32	no	—
516	D₄	—	316	16	no	—
517	D₄	—	158	64	no	—
518	D₄	—	158	32	no	—
519	D₄	—	158	32	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	16	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	16	no	—
524	C₂×C₄	—	316	16	no	—
525	C₂×C₄	—	316	32	no	—
526	C₂×C₄	—	316	8	no	—
527	C₂×C₄	—	79	8	no	—
528	C₂×C₄	—	79	8	no	—
529	C₂×C₄	—	158	32	no	—
530	C₂×C₄	—	158	8	no	—
531	C₂×C₄	—	158	16	no	—
532	C₂×C₄	—	158	8	no	—
533	C₂×C₄	C₂⁴×D₇₉	1	16	yes	—
534	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
535	C₂²	—	2	16	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	4	16	no	—
540	C₂²	—	316	16	no	—
541	C₂²	—	316	64	no	—
542	C₂²	—	316	8	no	—
543	C₂²	—	316	16	no	—
544	C₂²	—	79	8	no	—
545	C₂²	—	632	16	no	—
546	C₂²	—	158	32	no	—
547	C₂²	—	158	8	no	—
548	C₂²	—	158	4	no	—
549	C₂²	—	158	16	no	—
550	C₂²	—	158	8	no	—
551	C₂²	—	158	16	no	—
552	C₂²	—	158	4	no	—
553	C₂²	—	158	4	no	—
554	C₂²	C₂²×#11929625	1	8	yes	—
555	C₂²	C₂²×#11929625	1	4	yes	—
556	C₂²	C₂²×#11929625	1	2	yes	—
557	C₂²	H(5,𝔽₂)×D₇₉	1	4	yes	—
558	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
559	C₄	—	2	8	no	—
560	C₄	—	2	16	no	—
561	C₄	—	158	8	no	—
562	C₄	—	158	8	no	—
563	C₂	—	2	8	no	—
564	C₂	—	2	4	no	—
565	C₂	—	316	4	no	—
566	C₂	—	316	8	no	—
567	C₂	—	158	8	no	—
568	C₂	#23777090	1	4	yes	direct product factor
569	C₂	C₂³×#11929625	1	1	yes	characteristic
570	C₂	C₂×H(5,𝔽₂)×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#543×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#543	D₇₉
hypocenter	C₇₉	C₂×#3490
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#543

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #23777090	C₂	direct (N × H)
2. C₂×#19099240	C₂	semidirect
3. C₂×#19099204	C₂	semidirect
4. C₂×#19099153	C₂	semidirect
5. C₂×#19099125	C₂	semidirect
6. C₂×#19099076	C₂	semidirect
7. C₂²×#14579131	C₂	semidirect
8. C₂×#19099036	C₂	semidirect
9. C₂²×C₂²⋊C₄×D₇₉	C₂	semidirect
10. C₂×#543×C₇₉	C₂	semidirect
12. C₂²×#11929625	C₂²	semidirect
13. C₂³×D₃₁₆	C₂²	semidirect
15. C₂³×C₄×D₇₉	C₂²	semidirect
16. #19099240	C₂²	semidirect
17. #19099204	C₂²	semidirect
18. #19099153	C₂²	semidirect
19. #19099125	C₂²	semidirect
20. C₂×#14579156	C₂²	semidirect
21. C₂×#14579150	C₂²	semidirect
22. #19099076	C₂²	semidirect
23. C₂×#14579146	C₂²	semidirect
24. C₂×#14579146	C₂²	semidirect
25. C₂×#14579145	C₂²	semidirect
26. C₂×#14579137	C₂²	semidirect
27. C₂×#14579136	C₂²	semidirect
28. C₂×#14579136	C₂²	semidirect
29. C₂×#14579135	C₂²	semidirect
31. C₂×#14579131	C₂²	semidirect
32. C₂×#14579131	C₂²	semidirect
33. C₂×#14579131	C₂²	semidirect
34. C₂×#14579131	C₂²	semidirect
35. #19099036	C₂²	semidirect
36. C₂×#14579123	C₂²	semidirect
37. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
38. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
39. C₂×#14579119	C₂²	semidirect
40. C₂×#14579117	C₂²	semidirect
42. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
43. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
44. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
45. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
46. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
47. #543×C₇₉	C₂²	semidirect
48. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
49. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
60. C₂×#11929625	C₂³	semidirect
64. C₂²×D₃₁₆	C₂³	semidirect
65. C₂²×D₃₁₆	C₂³	semidirect
75. C₂²×C₄×D₇₉	C₂³	semidirect
76. C₂²×C₄×D₇₉	C₂³	semidirect
77. #14579156	C₂³	semidirect
78. #14579150	C₂³	semidirect
79. #14579146	C₂³	semidirect
80. #14579146	C₂³	semidirect
81. #14579145	C₂³	semidirect
82. #14579137	C₂³	semidirect
83. #14579136	C₂³	semidirect
84. #14579136	C₂³	semidirect
85. #14579135	C₂³	semidirect
87. #14579131	C₂³	semidirect
88. #14579131	C₂³	semidirect
89. #14579131	C₂³	semidirect
90. #14579123	C₂³	semidirect
91. C₄×C₂²⋊D₇₉	C₂³	semidirect
92. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
93. #14579119	C₂³	semidirect
94. #14579117	C₂³	semidirect
95. C₂×C₄⋊Dic₇₉	C₂³	semidirect
96. C₂×Dic₇₉⋊C₄	C₂³	semidirect
102. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
103. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
104. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
105. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
106. C₂²⋊C₄×D₇₉	C₂³	semidirect
107. C₂²⋊C₄×D₇₉	C₂³	semidirect
108. C₂×C₄×Dic₇₉	C₂³	semidirect
110. C₂²×Q₈×C₇₉	C₂³	semidirect
113. C₂²⋊Q₈×C₇₉	C₂³	semidirect
114. C₂²⋊Q₈×C₇₉	C₂³	semidirect
115. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
116. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
148. C₂×D₃₁₆	C₂⁴	semidirect
166. C₂×C₄×D₇₉	C₂⁴	semidirect
167. C₄⋊Dic₇₉	C₂⁴	semidirect
168. Dic₇₉⋊C₄	C₂⁴	semidirect
173. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
174. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
175. C₄×Dic₇₉	C₂⁴	semidirect
177. C₂⁴×C₇₉	#41	semidirect
182. C₂×Q₈×C₇₉	C₂⁴	semidirect
189. C₄⋊C₄×C₇₉	C₂⁴	semidirect
190. C₄⋊C₄×C₇₉	C₂⁴	semidirect
200. C₂³×C₇₉	C₂×#41	semidirect
280. C₂×C₇₉	#3490	semidirect
289. C₂×#543	D₇₉	semidirect
296. C₇₉	C₂×#3490	semidirect
304. #543	C₂×D₇₉	semidirect
314. C₂×C₂²⋊Q₈	C₂×D₇₉	semidirect
315. C₂×C₂²⋊Q₈	C₂×D₇₉	semidirect
348. C₂²×Q₈	C₂²×D₇₉	semidirect
373. C₂²⋊Q₈	C₂²×D₇₉	semidirect
374. C₂²⋊Q₈	C₂²×D₇₉	semidirect
389. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
390. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
428. C₂⁴	#11929625	semidirect
434. C₂×Q₈	C₂³×D₇₉	semidirect
468. C₄⋊C₄	C₂³×D₇₉	semidirect
469. C₄⋊C₄	C₂³×D₇₉	semidirect
510. C₂³	C₂×#11929625	semidirect
568. C₂	#23777090	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23777090	2
C₂×#19099240	2
C₂×#19099204	2
C₂×#19099153	2
C₂×#19099125	2
C₂×#19099076	2
C₂²×#14579131	2
C₂×#19099036	2
C₂²×C₂²⋊C₄×D₇₉	2
C₂×#543×C₇₉	2
C₂×#3490	79

Subgroups — C2×#23777090 #35196183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777090 #35196183